The present invention relates generally to communication systems and, in particular, to joint detection of a coded signal in a CDMA system.
FIG. 1 depicts a discrete time baseband model 100 of a known CDMA system that supports K block transmission users. These users have simultaneous access to the same physical, frequency-defined channel and transmit data block by block, each block having N symbols. Each user, 1 through K, has a sequence of information bits, d(1) through d(K), to be transmitted. Each user""s sequence is first turbo encoded and mapped to channel symbol sequences s(1) through s(K) respectively. These channel symbol sequences are then spread by their corresponding code C(1) through C(K), each of which has Q random chips, and passed through their corresponding channel, characterized by impulse responses h(1) through h(K) with W taps at chip level. For simplicity, it is assumed that this system uses BPSK modulation, so s(1) through s(K) are sequences of 1 and xe2x88x921, and the physical channel is an additive white Gaussian noise (AWGN) channel.
At the receive end, the received signal r can be expressed:                     r        =                                            ∑                              k                =                1                            K                        ⁢                          xe2x80x83                        ⁢                                          s                                  (                  k                  )                                            ⁢                                                C                                      (                    k                    )                                                  ⊗                                  h                                      (                    k                    )                                                                                +          n                                        =                  As          +          n                    
where r is a summation of K sequences and n represents channel noise, each of the length (NQ+Wxe2x88x921). A is a (NQ+Wxe2x88x921) by NK matrix consisting of:
a(k)=(a1(k),a2(k), . . . , aQ+Wxe2x88x921(k))=C(k)h(k)
and s is a composite symbol vector combining all symbols of the K users and arranged in the following order:
s=(s1(1),s1(2), . . . ,s1(K),s2(1),s2(2), . . . ,s2(K),s3(1), . . . ,sN(1), . . . ,sN(K))T
where T denotes the transposition operation. The received signal r is passed through a bank of matched filters, each one matches a(k). The output of the matched filter bank, y, is a minimum sufficient statistic of transmitted signals for all K users and can be expressed as:
xe2x80x83y=AHr=AHAs+z=Rs+z
where y, s, and z are NK by 1 vectors, and R is an NK by NK block toeplitz matrix. By using Cholesky factorization, R can be written as:
R=LLH=LnDLnH
where L is a lower triangular matrix, Ln denotes a normalized L in which all elements of the diagonal are ones, and D represents a diagonal matrix.
Joint detection is known to be an optimal receiver for CDMA systems. One well-known joint detector is implemented using a zero-forcing block linear equalizer (ZF-BLE). Its output may be expressed as:
sZF-BLE=Rxe2x88x921y=Lxe2x88x92HLxe2x88x921y=Lnxe2x88x92HDxe2x88x92xc2xdLxe2x88x921y
In practice, inversion of lower and upper triangular matrices can be achieved by forward and backward substitution. Therefore, by using Cholesky factorization, no actual matrix inversion is needed for joint detection. Another well-known joint detection technique, zero-forcing block decision feedback equalization (ZF-BDFE), is derived from ZF-BLE by using quantized previous samples, according to the symbol alphabet, in the backward substitution corresponding to the operation of Lnxe2x88x92H.
With regard to performance, ZF-BLE joint detection suffers from noise enhancement and thus performs very poorly in bad channel conditions where frequency response has a deep notch. ZF-BDFE joint detection does not have this drawback and therefore usually outperforms ZF-BLE joint detection. However, since the hard decision in conventional ZF-BDFE joint detection is generated by a simple slicer, the performance of ZF-BDFE joint detection will also degrade if the received signal-to-noise-ratio (SNR) is low. Because of its many performance advantages, 3rd generation (3G) mobile systems will use turbo encoded signaling. However, turbo encoded signaling exhibits a low SNR. Thus, a method and apparatus for joint detection of coded signaling in CDMA systems is needed to address the deficiencies of the prior art joint detection techniques, especially with respect to 3G systems.